application/xmlStudy of the pionic enhancement in [formula omitted] at 295 MeVT. WakasaG.P.A. BergH. FujimuraK. FujitaK. HatanakaM. IchimuraM. ItohJ. KamiyaT. KawabataY. KitamuraE. ObayashiH. SakaguchiN. SakamotoY. SakemiY. ShimizuH. TakedaM. UchidaY. YasudaH.P. YoshidaM. YosoiIsovector [formula omitted] stateHigh resolution measurementPionic enhancementSpin-longitudinal responseLandau–Migdal parametersPhysics Letters B 632 (2006) 485-489. doi:10.1016/j.physletb.2005.11.009journalPhysics Letters BCopyright © 2005 Elsevier B.V. All rights reserved.Elsevier B.V.0370-2693632419 January 20062006-01-19485-48948548910.1016/j.physletb.2005.11.009http://dx.doi.org/10.1016/j.physletb.2005.11.009doi:10.1016/j.physletb.2005.11.009http://vtw.elsevier.com/data/voc/oa/OpenAccessStatus#Full2014-01-01T00:14:32ZSCOAP3 - Sponsoring Consortium for Open Access Publishing in Particle Physicshttp://vtw.elsevier.com/data/voc/oa/SponsorType#FundingBodyhttp://creativecommons.org/licenses/by/3.0/JournalsS300.2PLB22573S0370-2693(05)01620-510.1016/j.physletb.2005.11.009Elsevier B.V.ExperimentsFig. 1The measurement of the cross section (left panel) and the analyzing power (right panel) for O16(p,p) at Tp=295MeV. The solid curves are the theoretical predictions using the global OMP for 16O. The dashed curves represent the results with the modified OMP as explained in the text.Fig. 2The excitation energy spectrum for O16(p,p′) at Tp=295MeV and qc.m.=1.9fm−1. The curves show the reproduction of this spectrum with hyper-Gaussian and Lorentzian peaks and a continuum.Fig. 3The measurement of the cross section of O16(p,p′)O16(0−,T=1) at Tp=295MeV. The solid (dash-dotted) curve is the DWIA result with the t-matrix parametrized at 325 (270) MeV employing the SM wave function in the 0s–0p–1s0d–1p0f model space. The dashed curve denotes the DWIA result with the t-matrix at 325 MeV employing the pure 0p1/21s1/2 SM wave function. The dotted curve represents the DWIA result with the modified OMP as described in the text.Fig. 4Comparison between experimental and theoretical cross sections of O16(p,p′)O16(0−,T=1) at Tp=295MeV. The dotted and dashed curves represent the DWIA results with the free response function employing m∗(0)=mN and m∗(0)=0.7mN, respectively. The solid curve denotes the DWIA result employing the RPA response function with gNN′=0.7, gNΔ′=0.4, and m∗(0)=0.7mN.Study of the pionic enhancement in O16(p,p′)O16(0−,T=1) at 295 MeVT.Wakasaa⁎wakasa@phys.kyushu-u.ac.jpG.P.A.Bergb1H.FujimuracK.FujitadK.HatanakadM.IchimuraeM.ItohfJ.KamiyagT.KawabatahY.KitamuradE.ObayashidH.SakaguchicN.SakamotodY.SakemidY.ShimizudH.TakedaiM.UchidajY.YasudacH.P.YoshidakM.YosoidaDepartment of Physics, Kyushu University, Fukuoka 812-8581, JapanbKernfysisch Versneller Instituut, Zernikelaan 25, 9747 AA Groningen, The NetherlandscDepartment of Physics, Kyoto University, Kyoto 606-8502, JapandResearch Center for Nuclear Physics, Osaka University, Osaka 567-0047, JapaneFaculty of Computer and Information Sciences, Hosei University, Tokyo 184-8584, JapanfCyclotron and Radioisotope Center, Tohoku University, Miyagi 980-8578, JapangAccelerator Group, Japan Atomic Energy Research Institute, Ibaraki 319-1195, JapanhCenter for Nuclear Study, The University of Tokyo, Tokyo 113-0033, JapaniThe Institute of Physical and Chemical Research, Saitama 351-0198, JapanjDepartment of Physics, Tokyo Institute of Technology, Tokyo 152-8550, JapankResearch and Development Center for Higher Education, Kyushu University, Fukuoka 810-8560, Japan⁎Corresponding author.1Present address: Department of Physics, University of Notre Dame, IN, USA.Editor: D.F. GeesamanAbstractThe cross section of the O16(p,p′)O16(0−,T=1) scattering was measured at a bombarding energy of 295 MeV in the momentum transfer range of 1.0fm−1⩽qc.m.⩽2.1fm−1. The isovector 0− state at Ex=12.8MeV is clearly separated from its neighboring states owing to the high energy resolution of about 30 keV. The cross section data were compared with distorted wave impulse approximation (DWIA) calculations employing shell-model wave functions. The observed cross sections around qc.m.≃1.7fm−1 are significantly larger than obtained by these calculations, suggesting pionic enhancement as a precursor of pion condensation in nuclei. The data are well reproduced by DWIA calculations using random phase approximation response functions including the Δ isobar that predict pionic enhancement.PACS25.40.Ep21.60.Jz27.20.+nKeywordsIsovector 0− stateHigh resolution measurementPionic enhancementSpin-longitudinal responseLandau–Migdal parametersThe search for pionic enhancements in nuclei has a long and interesting history. These phenomena can be considered as a precursor of the pion condensation [1] that would be realized in neutron stars. Enhancements of the M1 cross section in proton inelastic scattering [2–5] and of the ratio RL/RT, the spin-longitudinal (pionic) response function RL to the spin-transverse (non-pionic) response function RT, in the quasielastic scattering (QES) region [6,7] were expected around a momentum transfer qc.m.≃1.7fm−1. However, experimental data such as the differential cross section of the M1 transition C12(p,p′)C12(1+,T=1)[8] and the ratio RL/RT extracted from C12,Ca40(p→,n→)[9,10] did not reveal any enhancements, and they were considered as evidences against the precursor phenomena of the pion condensation in normal nuclei. Several explanations exist to answer the question why no pionic enhancements were observed. For example, Bertsch et al. [11] suggest the modification of gluon properties in the nucleus that suppresses the pion field. Brown et al. [12] suggest the partial restoration of chiral invariance with density. However, we should note that the M1 cross section involves both the pionic and the non-pionic transitions, and similarly the non-pionic response RT is equally important to determine the ratio RL/RT. Thus, in these indirect measurements, the pionic enhancement might be masked by the contribution from the non-pionic component. Recent analysis of the QES data [13] shows a pionic enhancement in the spin-longitudinal cross section that well represents the RL, and suggests that the lack of enhancements of RL/RT is due to the non-pionic component.In order to measure the pionic enhancement directly, it is desirable to investigate isovector Jπ=0−, 0±→0∓ excitations because they carry the same quantum numbers as the pion and they are free from non-pionic contributions in the direct channel. Orihara et al. [14] measured the angular distribution of the O16(p,n)F16(0−) reaction at Tp=35MeV. They reported discrepancies between distorted wave Born approximation calculations and their data in the range of qc.m.=1.4–2.0fm−1 that might be a signature of pionic enhancement. However, in both the O16(p,p′)O16(0−,T=1) scattering at Tp=65MeV[15] and the O16(p,n)F16(0−) reaction at Tp=79MeV[16], such an enhancement was not observed. The differences in these (p,n) and (p,p′) results might indicate contributions from complicated reaction mechanisms at these low incident energies. To our knowledge, there are no published experimental data for the 0−, T=1 state at intermediate energies of Tp>100MeV where reaction mechanisms are expected to be simple.In this Letter, we present the measurement of the cross section for the excitation of the 0−, T=1 state at Ex=12.8MeV in 16O using inelastic proton scattering at 295 MeV incident energy. The results are compared with distorted wave impulse approximation (DWIA) calculations using shell-model (SM) wave functions. A possible evidence of the pionic enhancement is observed from a comparison between experimental and theoretical results. The data are also compared with DWIA calculations employing random phase approximation (RPA) response functions including the Δ isobar in order to assess the pionic enhancement quantitatively.The measurement was carried out by using the west–south beam line (WS-BL) [17] and the Grand Raiden (GR) spectrometer [18] at the Research Center for Nuclear Physics, Osaka University. The WS-BL provides the beam with lateral and angular dispersions of 37.1 m and −20.0rad, respectively, which satisfy the dispersion matching conditions for GR, necessary for high momentum and angle resolutions. The beam bombarded a windowless and self-supporting ice (H2O) target [19] with a thickness of 14.1 mg/cm2. Protons scattered from the target were momentum analyzed by the high-resolution GR spectrometer with a resolution of about 30 keV FWHM. The beam energy was determined to be 295±1MeV by using the kinematic energy shift between elastic scattering from 1H and 16O. The yields of the scattered protons were extracted using the peak-shape fitting program Allfit[20].The elastic differential cross sections on 16O are shown in the left panel of Fig. 1. They were normalized to the known p+p cross section [21] by utilizing the data of protons scattered from 1H in the ice target. The analyzing power was also measured and the results are shown in the right panel. The data were analyzed by phenomenological optical model potentials (OMPs). The solid curves in Fig. 1 are the results using the global OMP optimized for 16O [22]. The dashed curves represent the results with the modified real and imaginary spin–orbit potentials by a factor of 1.15. The modified OMP gives a better description of our data especially for the cross sections at large momentum transfers.Fig. 2 shows the excitation energy spectrum of the O16(p,p′) scattering at qc.m.=1.9fm−1. The isovector 0− state at Ex=12.8MeV is clearly resolved from the neighboring states. The dashed curves represent the fits to the individual peaks while the straight line and solid curve represent the background and the sum of the peak fitting, respectively. Narrow peaks of 16O were described by a standard hyper-Gaussian line shape, and the peaks with intrinsic widths were described as Lorentzian shapes convoluted with a resolution function based on the narrow peaks. The positions and widths were taken from Ref. [23].Fig. 3 shows the measured data points and the calculated curves of the cross sections of the 0−, T=1 transition in O16(p,p′) as a function of the momentum transfer qc.m.. The angular distribution was measured in the range of qc.m.≃1.0fm−1 to ≃2.1fm−1 starting near the second maximum at qc.m. ≃0.9fm−1 and extending beyond the third maximum at qc.m. ≃1.7fm−1. The data at qc.m.<0.9fm−1 could not be measured because of the kinematic overlap with the p+p events. The error bars of the data points are the fitting uncertainties originating from the statistical uncertainties. The shaded areas represent the systematic uncertainties including the background subtraction.We performed DWIA calculations by using the computer code dwba98[24]. The one-body density matrix elements (OBDME) for the isovector 0− transition of O16(p,p′) were obtained from SM calculations [25] which were performed in the 0s–0p–1s0d–0f1p configuration space by using phenomenological effective interactions. In the calculation, the ground state of 16O was described as a mixture of 0ℏω (closed-shell) and 2ℏω configurations. The single particle wave functions were generated by a Woods–Saxon (WS) potential with r0=1.27fm−1 and a0=0.67fm−1[26], the depth of which was adjusted to reproduce the separation energies of the 0p1/2 orbits. The unbound single particle states were assumed to have a very small binding energy of 0.01 MeV to simplify the calculations. The NN t-matrix parametrized by Franey and Love [27] at 325 MeV was used. The DWIA results with the global and the modified OMPs are shown as the solid and the dotted curves, respectively, in Fig. 3. The results are insensitive to the OMP, and thus we will use the global OMP in the following. None of the calculations reproduce the data. Especially, note the underestimation around the third peak, which appears at about qc.m.≃1.7fm−1 in the experiment, but about qc.m.≃1.8fm−1 in the calculation.We investigated the sensitivity of the DWIA calculations to changes of the parameters involved. The dash-dotted curve represents the DWIA calculation with a different t-matrix parametrized at 270 MeV. The result is systematically larger compared to the calculation with the t-matrix at 325 MeV. The dash-dotted curve is, therefore, multiplied by a factor of 0.7. The dashed curve denotes the calculation employing a different OBDME with a pure 0p1/2−11s1/2 transition from the 0ℏω (closed-shell) ground state. Auerbach and Brown [25] suggest that this isovector strength is quenched and spread by a 2ℏω admixture. They obtained a quenching factor of ∼0.64. Thus we have multiplied our result by this factor. We also performed a DWIA calculation with the radial wave functions generated by a harmonic oscillator potential with a size parameter of α=0.588fm−1[28]. The result is systematically larger compared to the calculation with the WS potential. However, their shapes of the angular distribution are very similar to each other. From these calculations we found that the experimental data could not be reproduced well by changing the input parameters within the framework of the DWIA employing SM wave functions.Therefore, we investigated the non-locality of the nuclear mean field by a local effective mass approximation [10] in the form of(1)m∗(r)=mN−fWS(r)fWS(0)(mN−m∗(0)), where mN is the nucleon mass and fWS(r) is a WS radial form. The calculations were performed using the computer code crdw developed by the Ichimura group [29]. The dotted and dashed curves in Fig. 4 show the DWIA results with the free response function employing m∗(0)=mN and m∗(0)=0.7mN, respectively. The 0− component of the free response is configured as a pure 0p1/2−11s1/2 transition with a normalization factor of 0.64. The DWIA result with m∗(0)=mN is in good agreement with the calculation employing the corresponding SM wave function represented by the dashed curve in Fig. 3. Thus we have applied the same normalization factor of 0.64 to all the calculations shown in Fig. 4. The angular distribution shifts to lower qc.m. when decreasing m∗(0). A value of m∗(0)≃0.7mN[30,31] improves the agreement with the data, especially for the angular distribution. However there is still a large discrepancy between experimental and theoretical results around qc.m.≃1.7fm−1.Considering these analyses, we finally discuss the RPA correlation and Δ effects. We performed DWIA calculations with the RPA response functions employing the π+ρ+g′ model interaction Veff and the meson parameters from a Bonn potential which treats the Δ explicitly [32]. The interaction Veff is the sum of the one-π and one-ρ exchange interactions, and the Landau–Migdal (LM) interaction VLM specified by the LM parameters, gNN′, gNΔ′, and gΔΔ′, as(2)VLM=[fπNN2mπ2gNN′(τ1⋅τ2)(σ1⋅σ2)+fπNNfπNΔmπ2gNΔ′{((τ1⋅T2)(σ1⋅S2)+(τ1⋅T2†)(σ1⋅S2†))+(1↔2)}+fπNΔ2mπ2gΔΔ′{((T1⋅T2)(S1⋅S2)+(T1⋅T2†)(S1⋅S2†))+h.c.}]δ(r1−r2), where σ(τ) is the nucleon Pauli spin (isospin) matrix, S(T) is the spin (isospin) transition operator that excites N to Δ, fπNN(fπNΔ) is the πNN(πNΔ) coupling constant, and mπ is the pion mass. The LM parameters have been estimated to be gNN′=0.7±0.1 and gNΔ′=0.4±0.1[13]. The solid curve in Fig. 4 shows the DWIA result with gNN′=0.7, gNΔ′=0.4, and m∗(0)=0.7mN. This calculation reproduces the experimental data reasonably well. It shows large enhancement around qc.m.≃1.7fm−1, reflecting the pionic enhancement. Here we fixed gΔΔ′=0.5[33] since the gNΔ′ dependence of the results is very weak. Around qc.m.≃1.7fm−1, Veff with these LM parameters is close to zero in the NN channel, but very attractive in the NΔ channel [13]. This attraction causes the pionic enhancement.Before concluding the present analysis, we also considered effects of two-step contributions and isospin mixing in the 0− state. The following two-step processes are evaluated by the computer code twofnr[34]. (1) Excitation of the 0− state via a 3−, 0p1/2−10d5/2 state [35] was added to the direct 0−, 0p1/2−11s1/2 excitation in the transition amplitudes. The OBDME for the 3− transition was normalized to the described SM calculation, and the collective nature of the 3− state was taken into account by a renormalization factor of 2 [35]. It was found that by including the two-step process the cross section was reduced not more than about 3% in the present momentum transfer range. (2) The two-step excitation via the nucleon pickup-stripping reaction, namely (p,d)(d,p′) and (p,He2)(He2,p′), was evaluated and the effect was found also to be a reduction of less than about 3%. Note that both proton-pickup-stripping and neutron-pickup-stripping should be considered simultaneously to reflect the isospin nature correctly. As for the isospin mixing, we do not have reliable calculations about the isospin mixing of the 0−, Ex=12.80MeV state. If we take about 5% mixing of T=0 states from a simple estimation by Barker [36], the mixing effect on the DWIA result was found to be a reduction of about 25%. This reduction can be overcome if we choose the smaller LM parameters, gNN′≃0.6 and gNΔ′≃0.3.In conclusion, our high-resolution measurement of O16(p,p′)O16(0−,T=1) has enabled us to search for a pionic enhancement at an intermediate energy of Tp=295MeV where the theoretical DWIA calculations should be reliable owing to the simple reaction mechanism. A significant enhancement has been observed around qc.m.≃1.7fm−1 compared to the DWIA calculations with the SM wave functions and the local effective mass. The DWIA calculation employing the RPA response function with gNN′=0.7, gNΔ′=0.4, and m∗(0)=0.7mN reproduces the experimental data fairly well. Isospin mixing requires further enhancement of the pionic response function. The present analysis of our new measurement indicates the presence of the pionic enhancement in nuclei. However, further measurements for qc.m.<0.9fm−1 as well as more detailed theoretical analyses are needed to confirm this indication.AcknowledgementsWe thank the RCNP cyclotron crew for providing a good quality beam. This work was supported in part by the Grants-in-Aid for Scientific Research Nos. 12740151 and 14702005 of the Ministry of Education, Culture, Sports, Science, and Technology of Japan.References[1]A.B.MigdalSov. Phys. JETP3419721184Zh. Eksp. Teor. Fiz.6119712210(in Russian)[2]H.TokiW.WeisePhys. Rev. 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